# Center is marginal of finite type

From Groupprops

This article gives the statement, and possibly proof, of the fact that for any group, the subgroup obtained by applying a given subgroup-defining function (i.e., center) always satisfies a particular subgroup property (i.e., marginal subgroup of finite type)}

View subgroup property satisfactions for subgroup-defining functions View subgroup property dissatisfactions for subgroup-defining functions

## Statement

The center of a group is a marginal subgroup of finite type, and hence a marginal subgroup. More specifically, it is the marginal subgroup corresponding to the commutator word .